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If the problem sets are assigned from the book then the difficulty between doing them and the test is dramatic. Typically the assignment might be “do the even problems 2-14 on page X of the book”. However texts typically have to solutions in the back to 1/2 the problems, in this case I’ll assume the odd ones. So its possible to finish the problem sets by referring to the solutions of similar problems and by looking in the chapter, and still have no real understanding of the material. Then the test arrives, without the crutch of solved problems to refer to, and you’re stuck.</p>
<p>Added to this is the cumulative nature of math and science, where what you learn in class B strongly depends on the material in class A. Linear Algebra, which you said he did ok on, is one of the exceptions in math since its largely self-contained and you don’t need a large number of prerequisites to learn it. But in calculus, if you didn’t master the idea of substitution, for example, you’re going to be really lost when you move on to using trigonometric functions for substitution, and ready to throw up your hands when you are doing volumes & areas of revolution and need all those forms of substitution in order to solve the integrals. This may sound like gobbledy-gook but ask your son and I’m sure he can explain what it means! Again, the problem is that you can limp on using solved examples to guide you in the problem sets but be completely stumped on the tests. </p>
<p>And the classes move so fast that if you don’t learn something the first time thru their isn’t really time to go back and review it a month (or year) later; you have so much work to just get the labs and problem sets done.</p>
<p>So not knowing your son I’m going to make the following guess. He had enough native intelligence and drive to keep up in the math classes for a while, even though he wasn’t really mastering all the material. As time moved on the amount he really understood was dropping as were his test scores, but he kept trying to move forward. Eventually he ended up where he is today, where the current math classes are just too difficult. If he agrees with this assessment, then even if he does decide to stay in a technical field enrolling as a xfer somewhere else is not the right strategy at this point. He will simply be taking the same math courses somewhere else, with about the same results. He needs to figure out what he knows and what he doesn’t, and retake the math classes (even without getting college credit) at a CC or some other school and this time make sure he is understanding the material.</p>